相关论文: Elliptical Pursuit and Evasion -Extended Version-

Real-world physics can only be analytically modeled with a certain level of precision for modern intricate robotic systems. As a result, tracking aggressive trajectories accurately could be challenging due to the existence of residual…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

In the last years, a growing number of challenging applications in navigation, logistics, and tourism were modeled as orienteering problems. This problem has been proposed in relation to a sport race where certain control points must be…

Being able to anticipate the motion of surrounding agents is essential for the safe operation of autonomous driving systems in dynamic situations. While various methods have been proposed for trajectory prediction, the current evaluation…

To improve safety and energy efficiency, autonomous vehicles are expected to drive smoothly in most situations, while maintaining their velocity below a predetermined speed limit. However, some scenarios such as low road adherence or…

A modified lattice gas model is proposed to study pedestrian evacuation from a single room. The payoff matrix in this model represents the complicated interactions between selfish individuals, and the mean force imposed on an individual is…

This paper presents a new trajectory replanner for grasping irregular objects. Unlike conventional grasping tasks where the object's geometry is assumed simple, we aim to achieve a "dynamic grasp" of the irregular objects, which requires…

This paper solves a pursuit-evasion problem in which a prince must find a princess who is constrained to move on each day from one vertex of a finite graph to another. Unlike the related and much studied `Cops and Robbers Game', the prince…

Different sequences of ellipsoids are represented on the ellipticity-rotation plane. The rotation parameter is defined as the ratio of kinetic energy related to the mean tangential equatorial velocity component to kinetic energy related to…

Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…

The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several…

This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…

This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace,…

The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the 1D lattice random walk in discrete time. We determine the survival probability of the random walker in…

Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of…

This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate…

Mobile manipulators have been employed in many applications that are traditionally performed by either multiple fixed-base robots or a large robotic system. This capability is enabled by the mobility of the mobile base. However, the mobile…

Lenia is a continuous extension of Conway's Game of Life that exhibits rich pattern formations including self-propelling structures called gliders. In this paper, we focus on Asymptotic Lenia, a variant formulated as partial differential…

Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical…

Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…